However, no one likes actually seeing them in fantasy games. They're usually immune to damage or have high resistances to damage, they frequently dissolve armor or weapons, sometimes they themselves are poisonous, and even in the best case scenario, it's still just an awful pile and it probably doesn't have any treasure.
Okay, well, if the player's don't like them, lets at least make them have a fun combat mechanic. Here's a hack for nearly any RPG that uses hit points.
Okay, so, when a slime appears, make a little line of dice in front of you. The number of dice, and the size of the dice, depend on how many HP the slime has. You'll need to make the call yourself, but use dice that have numbers the PCs will have an easy time hitting with their damage output. Line up the dice so that the numbers visible add up to the total HP of the slime. Jumble them up a little, don't just make a line of sequential numbers. Example: The Slime King is an AD&D monster with 32 HP. I line up six d8s with the following faces: 8, 5, 4, 7, 2, 6. I know that several players have d8 damage weapons, so I'm confident that they can deal an amount of damage listed on the dice with regularity.
Okay, so next time someone hits the slime, if they deal an amount of damage exactly equal to one of the dice, remove that dice, leaving a small gap. If they deal damage but it doesn't match a dice, reduce the value of the leftmost dice, possibly to 0, in which case remove that dice and continue on to the next one until all damage is accounted for.
Whenever a dice is removed from between any other dice, the slime splits. Each slime has a number of HP equal to its collection of dice, but acts as normal and, assuming its attack is acid or poison based instead of a body slam, it deals normal damage. You can reduce physical assault based damage accordingly. Example: The King Slime has the following dice: 8, 5, 4, 7, 2, 6. It is struck by one of the player's for 7 damage, so the 7 faced d8 is removed. Now there are two slimes! One has 17 HP (8,5,4) and the other has 8 (2,6). Next round, the larger slime is struck for 6 damage. It's total HP is reduced (it's dice now read 2, 5, 4) but it does not split and create another slime. If it had instead been hit for 5 damage, it would have split into an 8 HP slime and a 4 HP slime, each of which only has one dice worth of hit points, and is too small to split.